The KAM theorem and renormalization group

DOI10.1017/S0143385708080450zbMath1160.37388arXiv0707.3438OpenAlexW2117412296MaRDI QIDQ3625417

Emiliano De Simone, Antti Kupiainen

Publication date: 5 May 2009

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.3438

Mathematics Subject Classification ID

Renormalization group methods applied to problems in quantum field theory (81T17) Renormalization group methods in equilibrium statistical mechanics (82B28) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items (5)

KAM theory in configuration space and cancellations in the Lindstedt series ⋮ Oscillator synchronisation under arbitrary quasi-periodic forcing ⋮ Renormalization of planar analytic saddles ⋮ An expansion of the homoclinic splitting matrix for the rapidly, quasiperiodically, forced pendulum ⋮ Resonant motions in the presence of degeneracies for quasi-periodically perturbed systems

Cites Work

• Quasi-linear flows on tori: Regularity of their linearization
• Critical Behavior of a KAM surface. I: Empirical results
• KAM theorem and quantum field theory
• Twistless KAM tori
• A renormalization group fixed point associated with the breakup of golden invariant tori
• KAM theorem revisited
• Compensations in small divisor problems
• CONSTRUCTION OF WHISKERS FOR THE QUASIPERIODICALLY FORCED PENDULUM
• Scaling for a Critical Kolmogorov-Arnold-Moser Trajectory
• TWISTLESS KAM TORI, QUASI FLAT HOMOCLINIC INTERSECTIONS, AND OTHER CANCELLATIONS IN THE PERTURBATION SERIES OF CERTAIN COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS: A REVIEW
• A RENORMALIZATION PROOF OF THE KAM THEOREM FOR NON-ANALYTIC PERTURBATIONS
• Renormalization group and the Melnikov problem for PDE's

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